Essentials of integration theory for analysis
Author(s)
Bibliographic Information
Essentials of integration theory for analysis
（Graduate texts in mathematics, 262）
Springer, c2011
Available at / 60 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
STR||32||10200021323129
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references and index
Description and Table of Contents
Description
'A Concise Introduction to the Theory of Integration' was once a best-selling Birkhauser title which published 3 editions. This manuscript is a substantial revision of the material. Chapter one now includes a section about the rate of convergence of Riemann sums. The second chapter now covers both Lebesgue and Bernoulli measures, whose relation to one another is discussed. The third chapter now includes a proof of Lebesgue's differential theorem for all monotone functions. This is a beautiful topic which is not often covered. The treatment of surface measure and the divergence theorem in the fifth chapter has been improved. Loose ends from the discussion of the Euler-MacLauren in Chapter I are tied together in Chapter seven. Chapter eight has been expanded to include a proof of Caratheory's method for constructing measures; his result is applied to the construction of Hausdorff measures. The new material is complemented by the addition of several new problems based on that material.
Table of Contents
-Preface.-1. The Classical Theory.-2. Measures. -3. Lebesgue Integration.-4. Products of Measures.-5. Changes of Variable.-6. Basic Inequalities and Lebesgue Spaces.-7. Hilbert Space and Elements of Fourier Analysis.-8. The Radon-Nikodym Theorem, Daniell Integration, and Caratheodory's Extension Theorem.-Index.
by "Nielsen BookData"
